Epidemic malaria dynamics in Ethiopia: the role of self-limiting, poverty, HIV, climate change and human population growth

Krsulovic, Felipe Augusto Maurin; Moulton, Timothy Peter; Lima, Mauricio; Jaksic, Fabian

doi:10.1186/s12936-022-04161-2

Table 1 The logistic model’s results for P. falciparum and P. vivax from 1985 to 1998 and from 1998 to 2007 without and with the lateral effects of per capita GDP (GDP), as a proxy of poverty, human density (Density), minimum temperature (Temperature), New HIV cases (HIV) and deaths related to civil conflicts (Battle)

From: Epidemic malaria dynamics in Ethiopia: the role of self-limiting, poverty, HIV, climate change and human population growth

Pathogen	Period	Model	Variables		Parameters				R²	AIC
Pathogen	Period	Model	Variables		Rmax	K	Q	a	R²	AIC
P. falciparum	1985–1998	1			1.82	549.87	0.467		0.499	25.011
P. falciparum	1985–1998	2	GDP		1.94	1503.45	0.44	− 4.87	0.501	24.147
P. falciparum	1985–1998	3	Density		1.94	856.05	0.44	− 5.934	0.483	24.605
P. falciparum	1985–1998	4	HIV		1.94	633.6	0.44	− 0.00016	0.438	24.58
P. falciparum	1985–1998	5	Temperature		1.94	125.07	0.44	35.63	0.477	24.824
P. falciparum	1985–1998	6	Battle		1.94	601.411	0.44	− 0.0017	0.5766	15.728
P. falciparum	1985–1998	7	Temperature	GDP	0.51	1588.33	0.44	− 0.3799	0.65	28.262
P. falciparum	1985–1998	8	Temperature	HIV	0.51	92.63	2.27	− 0.00019	0.734	14.662
P. falciparum	1985–1998	9	Temperature	Density	0.51	219.912	2.27	0.795	0.638	28.854
P. falciparum	1985–1998	10	Temperature	Battle	0.51	751.7	2.27	− 0.00021	0.478	10.865
P. falciparum	1985–1998	11	GDP	Density	0.51	519.81	2.27	0.0182	0.624	29.206
P. falciparum	1985–1998	12	GDP	HIV	0.51	628.9	2.27	7.12E–06	0.631	29.059
P. falciparum	1985–1998	13	GDP	Battle	0.51	751.3	2.27	− 1.2E–05	0.722	10.918
P. falciparum	1985–1998	14	HIV	Density	0.51	794.7	2.27	0.000291	0.421	13.449
P. falciparum	1985–1998	15	HIV	Battle	0.51	743.5	2.27	− 2.2E–08	0.747	10.763
P. falciparum	1985–1998	16	Density	Battle	0.51	751.9	2.27	− 0.00005	0.723	10.859
P. vivax	1985–1998	17			3.01	524	0.292		0.352	35.32
P. vivax	1985–1998	18	GDP		3.01	2143.56	0.319	− 8.27	0.784	33.971
P. vivax	1985–1998	19	Density		3.01	− 498.96	0.319	19.82	0.849	31.683
P. vivax	1985–1998	20	HIV		3.01	226.5	0.319	0.00059	0.867	30.662
P. vivax	1985–1998	21	Temperature		3.01	− 672.8	0.319	101.5	0.791	35.11
P. vivax	1985–1998	22	Battle		3.01	629.06	0.319	− 0.0054	0.507	23.015
P. vivax	1985–1998	23	Temperature	GDP	3.01	1784.74	0.319	− 0.546	0.79	34.762
P. vivax	1985–1998	24	Temperature	Density	3.01	− 517.495	0.319	1.715	0.845	31.21
P. vivax	1985–1998	25	Temperature	HIV	3.01	224.9	0.319	5.05E–05	0.865	30.635
P. vivax	1985–1998	26	Temperature	Battle	3.01	627.2	0.319	− 4.3E–05	0.548	23.054
P. vivax	1985–1998	27	GDP	Density	3.01	− 249.573	0.319	0.077	0.805	33.489
P. vivax	1985–1998	28	GDP	HIV	3.01	225.3	0.319	0.000031	0.868	30.743
P. vivax	1985–1998	29	GDP	Battle	3.01	629.6	0.319	− 2.7E–05	0.584	22.943
P. vivax	1985–1998	30	HIV	Density	3.01	186.2	0.319	− 0.00022	0.313	14.311
P. vivax	1985–1998	31	HIV	Battle	3.01	657.7	0.319	− 3.5E–07	0.343	17.232
P. vivax	1985–1998	32	Density	Battle	3.01	616.9	0.319	− 0.00008	0.596	23.321
P. falciparum	1998–2007	33			18.01	72.46	0.094		0.369	31.429
P. falciparum	1998–2007	34	GDP		0.47	− 614.852	2.061	4.38	0.611	29.549
P. falciparum	1998–2007	36	Density		0.47	2710.63	2.061	− 35.26	0.887	19.969
P. falciparum	1998–2007	37	HIV		0.47	8708	2.061	− 0.0091	0.942	14.247
P. falciparum	1998–2007	38	Temperature		0.47	1743.2	2.061	− 118.7	0.653	28.761
P. falciparum	1998–2007	39	Battle		0.47	237.395	2.061	0.0101	0.383	26.384
P. falciparum	1998–2007	40	Temperature	GDP	0.47	421.205	2.061	− 0.062	0.575	30.109
P. falciparum	1998–2007	41	Temperature	HIV	0.47	− 568.6	2.061	1.328	0.930	15.878
P. falciparum	1998–2007	42	Temperature	Density	0.47	2567.31	2.061	− 2641	0.901	19.122
P. falciparum	1998–2007	43	Temperature	Battle	0.47	2373	2.061	0.00087	0.383	26.381
P. falciparum	1998–2007	44	GDP	HIV	0.47	− 371.2	2.061	0.000062	0.882	20.291
P. falciparum	1998–2007	45	GDP	Density	0.47	2023.22	2.061	− 0.125	0.705	27.531
P. falciparum	1998–2007	46	GDP	Battle	0.47	237.4	2.061	0.000052	0.383	26.384
P. falciparum	1998–2007	47	HIV	Density	0.47	− 580.3	2.061	0.00023	0.941	15.345
P. falciparum	1998–2007	48	HIV	Battle	0.47	237.3	2.061	1.7E – 06	0.382	26.372
P. falciparum	1998–2007	49	Density	Battle	0.47	237.4	2.061	0.000152	0.384	26.388
P. vivax	1998–2007	50			0.5	185	0.094		0.401	20.519
P. vivax	1998–2007	51	GDP		0.5	1833.35	0.784	− 7.306	0.661	17.219
P. vivax	1998–2007	52	HIV		0.5	− 357.1	0.784	0.0016	0.789	16.364
P. vivax	1998–2007	53	Density		0.5	1379.7	0.784	− 15.47	0.527	18.912
P. vivax	1998–2007	54	Temperature		0.5	2822.9	0.784	− 199.8	0.602	17.76
P. vivax	1998–2007	55	Battle		0.5	203.054	0.784	0.247	0.406	13.341
P. vivax	1998–2007	56	Temperature	GDP	0.5	2627.7	0.784	− 0.908	0.822	13.245
P. vivax	1998–2007	57	Temperature	Density	0.5	1535.2	0.784	− 1.451	0.590	18.046
P. vivax	1998–2007	58	Temperature	HIV	0.5	6059	0.784	− 0.0005	0.757	14.159
P. vivax	1998–2007	59	Temperature	Battle	0.5	203.429	0.784	0.019	0.407	13.341
P. vivax	1998–2007	60	GDP	Density	0.5	1544.97	0.784	− 0.089	0.660	17.324
P. vivax	1998–2007	61	GDP	HIV	0.5	1455	0.784	− 6E–06	0.707	16.831
P. vivax	1998–2007	62	GDP	Battle	0.5	202.4	0.784	0.00129	0.406	13.368
P. vivax	1998–2007	63	HIV	Density	0.5	− 452.9	0.784	0.00217	0.837	12.56
P. vivax	1998–2007	64	HIV	Battle	0.5	205.9	0.784	3.5E–0 6	0.407	13.283
P. vivax	1998–2007	65	Density	Battle	0.5	201.2	0.784	0.0041	0.407	13.323

The results suggest a weak effect of minimum temperature to malaria dynamics for all periods and species. Models were compared and selected for each period and for each species based on high R² and lower AIC. From 1985 to 1998 for P. falciparum, the models 11, 13, 16 delivered the best results. For the same period and for P. vivax the models 25 and 28 delivered the best results. From 1998 to 2007 (P. falciparum) the models 37, 41 and 47 delivered the best results. From 1998 to 2007 (P. vivax) the models 56 and 63 delivered the best results. The logistic model without exogenous effects can be interpreted as a null model and models with exogenous effects as alternative models

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